Central banks have repeatedly revealed a preference for secrecy in
conducting monetary policy. In the United States, for example, the
Federal Reserve has expressed its bias towards policy secrecy in a
number of ways, ranging from delays in releasing the minutes of Federal
Open Market Committee (FOMC) meetings to ambiguous policy statements at
Congressional hearings. (1) Nevertheless, the degree of disclosure
required by Congress and the court system does not appear to minimize
central bank secrecy. Indeed, the Fed's right to limit disclosure
of policy intentions was upheld in a recent Supreme Court case. (2)
Furthermore, similar social tolerance of central bank secrecy appears in
the banking institutions of other countries.

Since legal and social institutions allow for central bank
secrecy, its presence may be attributed to the preferences of the social
planners who designed these institutions in the first place.
Forward-looking planners know that monetary policy in future periods
will be the outcome of a symbiotic relationship between monetary
authorities, politicians, and private interest groups. (3) As the
relative importance of these different groups and their preferences
change over time, so will the policy objectives of the monetary
authorities. If secrecy is allowed, monetary authorities could effect
policy changes in response to relationship changes without immediate
detection by private markets. Recognizing this policy effect of secrecy,
a social planner would design institutions to affect the environment so
that desirable future policy formation takes place. (4)

This paper offers two explanations for why social institutions do
not legally minimize central bank secrecy. (5) First, when establishing
institutional disclosure requirements for central banks, social planners
recognize the tendency for central bankers to be secretive. This secrecy
imposes costs upon members of society by making shifts in policy
objectives more difficult to detect. Faced with this tendency, members
of society set legal institutions that appear to require less
disclosure, because more restrictive laws would induce central bankers
to become more secretive in other, less informative, ways. (6)

Second, if the policy objectives that society finds desirable
change over time, then members of society may directly prefer some
degree of central bank secrecy. Economic theory holds that unanticipated
changes in monetary policy can have an economic effect. Intuitively,
secrecy allows central banks to conduct unanticipated policy actions in
periods when, on average, society most prefers them. For example, in
periods when public opinion favors pushing down unemployment, central
banks may conduct a surprise monetary expansion. (7)

The paper develops examples of each of these two effects using a
discretionary equilibrium similar to that in Cukierman and Meltzer
[1986a]. The desired trade-off between two policy objectives changes
over time in response to changing political pressures. Although I use
the trade-off between output and inflation as an example, the basic
results hold with any policy trade-off that varies over time. The policy
objectives could include targets for real exchange rates or interest
rates, for instance.

The plan of the paper is as follows. Section II describes the
discretionary equilibrium given institutional settings for the conduct
of monetary policy. Sections III and IV describe examples of each of the
two explanations for secrecy described above. Concluding remarks follow.

II. THE DEGREE OF POLICY DISCLOSURE IN A DISCRETIONARY
EQUILIBRIUM

When the policy objectives of the monetary authorities shift over
time due to changing economic or political circumstances, their choice
of discretionary policy also shifts. (8) In the absence of a mechanism
to pre-commit to a particular policy rule, the authorities will
implement policy changes. Furthermore, since central bankers cannot
precisely control the money supply over an indefinite time period, the
private market cannot directly observe the central bank's intended
policy. The interaction between changing policy objectives by central
banks, on the one hand, with incomplete private information about these
objectives, on the other, yields an equilibrium policy process. In this
equilibrium, market participants observe the money supply and other
variables that are correlated with central bank objectives in order to
form forecasts of future policy. In turn, central banks recognize that
market participants are watching current money and other variables when
deciding current policy. Within such a discretionary equilibrium, market
participants partially observe the central banker's policy
intentions by watching variables correlated with monetary policy.

But we must push this analysis back a step if we want to ask how
much central bank secrecy a social planner would prefer. Addressing this
question amounts to asking what kind of institutional environment
society would choose for the central bank to operate in, since this
environment implies a corresponding degree of implicit policy
disclosure.

This question will be the focus of sections III and IV below.
Before considering the secrecy issue, however, we must describe the
discretionary equilibrium given a particular institutional framework.
For this purpose, a discretionary equilibrium similar to Cukierman and
Meltzer [1986a] is briefly described next. (9)

The Central Bank's Objectives Given the Social Framework

As a policy-making entity, the government consists of many
individuals with objectives that depend upon the ability to stay in
office. Furthermore, the popularity of these government officials
depends upon key economic variables that affect the well-being of their
constituents. (10) For example, an over-valued exchange rate worsens the
competitiveness of the export industry, and high interest rates hurt the
housing market as well as debtors. Therefore, government officials are
influenced in their policy decisions by the effects of these policies
upon special interest groups.

Although government objectives depend upon a number of different
policy targets, I will take as an example the trade-off between two of
them. Specifically, the authorities would like to minimize inflation but
also use unanticipated inflation to reduce unemployment, as in Barro and
Gordon [1983]. Although this may not literally characterize central bank
behavior, I will use this well-known relationship to proxy for other
policy tradeoffs, such as exchange rates and interest rates. The
objective function of the central bank is then given by

where [m.sub.t] is the money supply at time t, [m.sup.c.sub.t] is the
money supply intended by central bankers, E(|[I.sub.t]) is the
expectations operator conditional upon the private sector's
information set at time t, and [x.sub.t] is the time-varying trade-off
between the first and second components in [W.sub.t]. The first
component says that central bankers would like to push up money,
[m.sub.t], for any given market forecast of money, since nominal wage
contracts incorporate expected inflation. A surprise expansion to the
money supply thus induces a surprise fall in real wages and an increase
in employment along the labor demand curve. The second component in (1)
says that central bankers do not like inflation.

The time-varying parameter [x.sub.t] represents the
authorities' policy trade-off between unemployment and inflation
targets. This trade-off captures the time-varying nature of the
symbiotic relationship between monetary authorities, politicians, and
interest groups. Changes in the distribution of income and political
power affect the influences upon the monetary authorities. Thus,
[x.sub.t] reflects the time-varying objectives that monetary authorities
pursue as an equilibrium response to political pressure. Note that the
objective function (1) is not a social welfare function, but rather the
objective function of the monetary authorities.

For the examples below, I characterize the changing objectives of
the monetary authorities according to the persistent process:

where [v.sub.t] is a serially uncorrelated random variable with zero
mean and constant variance, [[sigma].sup.2.sub.v]. The positive
parameter, A, is known to the private sector and reflects the
authorities' unconditional trade-off for expanding output relative
to reducing inflation. On the other hand, only the central bankers know
the time-varying component, [p.sub.t], at each point in time. The
disturbance, [v.sub.t], represents the most recent change in policy
objectives, [p.sub.t].

The preference pattern described in (2) implies that changes in
political trade-offs persist according to the autocorrelation parameter,
[theta]. This degree of persistence, in turn, depends upon social and
legal institutional settings. For instance, the terms of political
offices may overlap for individuals both inside and outside the central
bank who exert an influence on the authorities' policy-making
process.

The simple form of policy preferences in (2) provides a very
tractable and convenient solution to the discretionary equilibrium as
will be shown below. Despite its utter simplicity, this formulation yields a rich variety of implications regarding the persistence of
policy objectives. According to this process for [p.sub.t], any current
change in period t will also be correlated with the change in the
following period at t+l. The variance of next period's policy,
[p.sub.t] + 1, that can be explained by today's policy disturbance
is just equal to [theta]/(1 + [theta]). (11) Therefore, the
autocorrelation in the policy process, [theta], captures the component
of current policy preferences that will persist tomorrow.

The Discretionary Equilibrium

As a result of central bank secrecy, monetary authorities maintain
inside information about their policy objectives. Therefore, private
market participants can only watch variables correlated with these
objectives to make inferences about policy. Put into the context of the
objectives above, the market can observe the outcome of the money
supply, [m.sub.t], but only the central bank knows its current
objectives, [P.sub.t]. Based upon the current private information set,
market participants then try to detect [P.sub.t] in order to predict the
outcome of future policy.

In order to provide a simple solution, I will assume that past
disturbances to policy objectives, [v.sub.t-k], are observed with some
lag, k. Nevertheless, central bankers still have inside information,
since they alone know their current objectives, [v.sub.t], and therefore
[p.sub.t]. This simplification is not necessary for the results obtained
below but significantly streamlines the algebra. (12) Furthermore, this
assumption may be reasonable for the United States since the Fed
publishes its "Directive" of the past Federal Open Market
Committee meeting just prior to the current meeting.

For further simplicity, the policy revelation lag, k, is set equal
to one. Therefore, the information set available to the private sector
at the end of period t contains current and lagged money and lags of
policy objectives. That is, [I.sub.t] [equivalent to] {[m.sub.t],
[m.sub.t-1], [m.sub.t-2], ..., [v.sub.t-1], [v.sub.t-2], ...}. In
general, the information set may also contain other variables that are
correlated with policy objectives. For example, in section IV the
information set will be expanded to include public opinion. Since the
basic results remain when including these variables, I will first
consider the shorter information set.

Given these objectives, the monetary authorities choose the money
supply to maximize the discounted present value of equation (1). In
other words,

(3) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [m.sup.c.sub.t] is the authorities' planned money supply
and [G.sub.t] is the government's information set at time t that
includes the government's current preferences; i.e., [G.sub.t]
[equivalent to] ([v.sub.t], [v.sub.t-1], ...}. Although future economic
or political conditions are likely to have a high variance, the
government has better information about this outcome because it has
inside information about current policy.

The authorities can hide their current objectives because they
cannot perfectly control the money supply. That is, observed money
supply differs from the authorities' planned money supply according
to control noise,

(4) [m.sub.t] = [m.sup.c.sub.t] + [[phi].sub.t],

where [[phi].sub.t] is a serially uncorrelated random variable with
mean zero and variance [[sigma].sup.2.sub.[phi]]. Since the money supply
cannot be controlled precisely, the variance of the control error has a
lower bound so that [[sigma].sub.[phi]] [greater than or equal to]
[[??].sub.[phi]], where [[??].sub.[phi]] is the minimum possible
variance of the control error.

Private market participants form rational expectations about the
future money supply. As will be shown below, the private sector's
expectations are rational when they believe that the authorities use the
following rule to conduct monetary policy:

As quick inspection of (4) and (5) verifies, private agents observe
the composite term in parentheses in equation (7), but not its
components. Further substituting (7) into (6) above provides the
function that private agents use to forecast government policy:

That is, although agents cannot directly observe the money supply
intended by the authorities, [m.sup.c.sub.t-1]they forecast it
implicitly.

The authorities recognize that their choice of money affects the
market's forecasts as described in (8). Therefore, in maximizing
their own objectives in (3), they view equation (8) as a constraint.
Substituting (8) into (3) and maximizing with respect to [m.sup.c.sub.t]
yields the following first-order condition:

(9) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

This equation provides the equilibrium response of the government
given the market's beliefs. The central bankers know their own
objectives at time t, but have only a forecast about their objectives in
the next period. At each point in time, they would like to set the money
supply equal to the current period trade-offs, [x.sub.t]. But they know
that fully responding to these policy preferences would reveal them to
the private sector. Therefore, they do not fully respond to their
desired policy every period.

To find the equilibrium, we must equate the private sector's
beliefs about government policy in equation (5) to the government's
actual policy given private beliefs in equation (9). This provides the
equilibrium levels of the coefficients:

(10a) [B.sub.0] = [1 - [beta][theta]a([B.sub.1])

(10b) [B.sub.1] = [1 - [beta][[theta].sup.2]a([B.sub.1])

(10c) [B.sub.2] = [theta].

As these equations indicate, [B.sub.0] and [B.sub.1] depend upon the
expectations coefficient, a([B.sub.1]), which in turn depends upon
[B.sub.1]. Therefore, [B.sub.1] determines the rest of the equilibrium.
To focus upon choice variables, but without loss in generality, the rate
of time preference, [beta], will be set equal to one throughout the
remaining analysis.

Figure 1 illustrates the solution of [B.sub.1] in terms of the
intersection between market beliefs from equation (5) and the actual
policy from equation (10). The vertical axis shows the rule that the
authorities actually follow as a function of [B.sub.1], given by the
right-hand side of (10b). For given variances, [[sigma].sub.v] and
[[sigma].sub.[theta]], the policy function is described by the bold line
labeled 1 - [[theta].sup.2] a([B.sub.1], ...) and is minimized at B =
([[sigma].sub.v]/ [[sigma].sub.[theta]]). This function intersects with
the private market's beliefs, [B.sub.1], at point [B.sup.*.sub.1a].
The equilibrium between private market beliefs and government objectives
ties down the discretionary equilibrium.

The degree of variability in the market's forecast of policy
provides a useful measure of the monetary authorities' inherent
secrecy about policy objectives. Using the equilibrium solutions in (10)
above, the degree of "secrecy" inherent in any discretionary
equilibrium may be written: (13)

Thus, how much of the current policy objectives can be detected by
private agents depends both upon (a) the persistence of policy
objectives, deterring authorities from reacting to their current
preferences, and upon (b) the degree of monetary noise, allowing
authorities to hide their current policy actions. These variables are
not arbitrarily determined. Rather, they depend upon choices made when
designing the institutions for conducting monetary policy. To examine
how these institutions are chosen, along with their implied level of
secrecy, I consider two different social objective functions in the next
two sections.

III. SECRECY WHEN SOCIETY PREFERS STABLE POLICY

Social and legal institutions such as the Constitution are devised by
members of society who try to anticipate future policy pressures upon
government officials. Similarly, the members of society who originally
determined the institutions of central banks recognized that central
bankers would face different pressures over time. Therefore, the social
planners would have designed these institutions to influence future
policy outcomes in accord with their own objectives. This is illustrated
in the following example.

Suppose first that these social planners prefer a stable trade-off
between unemployment and inflation with an objective function given by

The difference between the policymakers' objectives and
society-as-a-whole's objectives can be seen by comparing equation
(12) with equation (1). Policymakers are influenced by individuals, such
as small interest groups or particular members of the FOMC, through the
variable [x.sub.t] in equation (1). (14)

From the social planners' viewpoint, the variability in the
discretionary equilibrium described above imposes costs. The absence of
a mechanism to force central bankers to commit to a stable policy rule
implies that the authorities will always follow the discretionary
policy. But some discretionary equilibria are socially preferable to
others, as the expected value of the planners objective function
demonstrates. Substituting the private sector money supply beliefs from
(5) into (12) and taking expectations yields,

This cost arises from two components that depend in turn upon A, the
unconditional tendency of the authorities to inflate, and upon
[[sigma].sub.v], the variability of policy shifts. Specifically, the
first component, 1/2 [B.sup.2.sub.0] [A.sup.2], gives the dead-weight
loss of a suboptimally high inflation level. The persistence of policy
deters the authorities from expanding so that the unemployment trade-off
term, A, depends upon a number less than one; i.e., [B.sub.0] = (1 -
a[theta]) < 1. By contrast, the second component, 1/2
([B.sup.2.sub.1] + [B.sup.2.sub.2]) [[sigma].sup.2.sub.v], captures the
effects of changing policy objectives upon the inflation variance. Other
things equal, more variability in policy pressures by special interest
groups induces greater variability in monetary policy and, therefore,
higher expected costs from the viewpoint of social planners.

Although discretionary government policy imposes these social
costs, society can influence the behavior of discretionary government
policy by its choice of the institutional environment. The degree of
policy persistence can be affected by a number of different social and
legal institutions that promote longer terms or overlaps of office for
governmental officials. For example, the U.S. Banking Act of 1935
instituted fourteen-year terms of appointment for Federal Reserve
governors with a turnover of one governor every two years. The purpose
of the measure was to make for smoother policy transitions and also to
reduce the governors' dependence upon the President who has a
shorter term of office. The average turnover in the governorship
positions has been about seven years.

Thus, if society could choose the rate of policy persistence to
minimize the costs of discretionary policy, how much persistence would
it choose? This question may be answered by considering a social planner
at the beginning of time who maximizes equation (13) with respect to
[theta]. This maximization is proven in the appendix and implies the
following result:

RESULT 1: For a given degree of policy noise, [[sigma].sup.[phi]],
the optimal degree of persistence in policy objectives is the highest
persistence possible: [[theta].sup.*] = 1.

Intuitively, we can see from equation (13) above that a change in
persistence will implicitly affect social welfare both through the level
and the variance of inflation. Figure 1 illustrates the effects of
changing upon the equilibrium levels of [B.sub.1] and, hence, through
(10a), [B.sub.0]. A rise in [theta] to [[theta].sub.1] >
[[theta].sub.0] will shift down the government's reaction function,
1 - [[theta].sup.2] a(x) at every level of [B.sub.1]. This implies a
lower level of equilibrium [B.sub.1] at [B.sub.1b.sup.*] <
[B.sub.1a.sup.*] and therefore less reaction to current policy
objectives and a lower level of [B.sub.0]. This deterrent upon changing
policy implies both a lower level of inflation through [B.sub.0], and a
lower variance of inflation through [B.sub.1]. For both reasons, society
would prefer policies that induce greater policy persistence.

The Government's Desire for Secrecy

Given the degree of policy noise inherent in the monetary
operating procedure, the result above says that society would set up
institutions that fostered the greatest policy persistence possible.
However, given greater stability of tenure in office, policymakers may
choose operating procedures that further obfuscate their policy
intentions. (15) To consider how the welfare of policymakers depends
upon their ability to hide policy intentions, we can calculate their
expected utility by substituting equation (5) into equation (1) and
taking expectations:

Comparing (14) to (13) reveals that the authorities'
objectives differ from those of the social planners because the planners
prefer smooth policy while the authorities would rather change policy in
response to political pressures. The inflation cost represents a cost to
both central bankers and social planners. This cost is given by the
first term in brackets and depends upon the average level of inflation,
[B.sub.0]A. However, by the second term, ([B.sup.2.sub.1] +
[B.sup.2.sub.2])[[sigma].sup.2.sub.v], the central bankers gain from the
variability of policy while society loses. To see why, note from (5)
that the authorities react to their current political pressures
according to the coefficients [B.sub.1] and [B.sub.2]. However, current
preferences, [P.sub.t], are correlated in equilibrium with the forecast
error by private agents, ([m.sub.t] - E([m.sub.t] | [I.sub.t-1]).
Therefore, the authorities gain from generally being able to surprise
the market with a monetary expansion during the periods when interest
groups and other agents in the symbiosis most care about increasing
output. But since social planners prefer smooth policy, they view this
variation in policy as costly.

As Cukierman and Meltzer [1986a] show, central bankers may prefer
greater monetary noise, [[sigma].sub.[phi]], so they can more easily
surprise the market with monetary expansions to stimulating the economy.
Intuitively, monetary noise allows the authorities to be ambiguous about
their policy intentions and to produce a greater shock to the economy
when [p.sub.t] is large. By determining the monetary policy environment,
such as in the choice of operating procedures, they influence the degree
of noise inherent in the money supply process. What level of noise would
the authorities choose? Maximizing equation (14) with respect to
[[sigma].sub.[phi]] for a given level of persistence, [theta], yields a
second result (which is proven in the appendix).

RESULT 2: For a given degree of policy persistence, the authorities
would choose a higher [a.sup.*.sub.[phi]] than the minimum possible
variance. Furthermore, the optimal variance, [[sigma].sup.*.sub.[phi]],
increases with policy persistence, [theta].

Intuitively, the higher the noise in monetary error, the more the
authorities can hide their current policy objectives, and the more, on
average, they can gain from surprise expansions.

Society's Choice of Persistence When Central Banks are
Secretive

The result above indicates that central bankers would prefer to be
more secretive, given a process for policy shifts. However, in
developing institutions for conducting monetary policy, social planners
recognize this tendency toward secrecy. Therefore, instead of simply
choosing institutions that promote policy persistence given the
noisiness of central bank policy, as in result 1, these planners
incorporate the choices made by central banks, as in result 2.

In terms of the example above, we can address this issue by
asking: How would a social planner's choice of policy persistence
change when he realizes that central banks will choose ambiguity based
upon this persistence? More specifically, totally differentiating
equation (14) with respect to [theta] and incorporating result 2 implies

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Result 1 said that society would maximize the first term on the
right-hand side, holding [[sigma].sub.[phi]], constant. However, result
2 says that ambiguity increases with the persistence; or, in other
words, (d[[sigma].sup.*.sub.[phi]]/d[theta])> 0. On the other hand,
social welfare falls as the variance of policy increases, i.e., (dE(U)/
d[[sigma].sub.[phi]]) (0. Therefore, although greater policy persistence
reduces variability and hence improves social welfare through the first
term, it also prompts central bankers to conceal their policies,
reducing welfare through the second term. This relationship leads to the
following result:

RESULT 3: Society chooses a lower rate of policy persistence when the
government decides the degree of policy ambiguity based upon this
persistence.

The result is formally derived in the appendix.

The example in this section also illustrates a more general point.
If society tries to constrain secrecy in one way, central bankers will
try to regain lost effectiveness by building up secrecy in other ways.
This means that in the design of social institutions, account must be
taken of the central bank's reactions to any constraints on
secrecy. We may therefore wind up accepting types of secrecy that appear
preventable because eliminating them or reducing them would lead to
higher costs due to the Fed's reaction.

IV. SECRECY WHEN SOCIETY PREFERS DISCRETIONARY POLICY

In contrast to the example above, suppose that social planners
anticipate that their future preferences for policy objectives may
change over time with changing economic circumstances. In this case,
society may directly prefer greater central bank secrecy. To illustrate,
suppose that instead of (13), social objectives can be written:

where [u.sub.t] = [e.sub.t] + [mu] [e.sub.t-1]. That is, public
opinion about the importance of unemployment relative to inflation
changes over time according to [u.sub.t]. This variable follows a
first-order moving average process as in the authorities objectives (2).
Furthermore, since changing social opinion about economic trade-offs
influences the authorities' popularity, shifts in public opinion
are correlated with shifts in government policies; i.e.,
E([v.sub.t][e.sub.t]) = [[sigma].sub.ve] > 0.

Therefore, since they know public opinion, private agents have an
additional piece of information about policy intentions. As a result,
the private sector's information set every period now includes the
most recent state of public opinion, [e.sub.t], so that it becomes,

In this case, the discretionary solution appears the same as
described in section I, except that the market's prediction of the
policy preferences now depends upon public opinion as well. Instead of
(7), we have

where now [??] < a, since agents pay relatively less attention to
money when making forecasts now that they have additional information.
Substituting this forecast of policy preferences into the money supply
forecast, the discretionary equilibrium can be calculated with the same
steps as in section II. Further substituting the money supply beliefs in
(5) into the objective function (16) gives the expected value of social
welfare as

The first term in brackets is the same as in equation (13). The
second term represents the cost arising from periods when society would
prefer more monetary stimulation. The last term increases social welfare
due to the covariance between public opinion and the preferences of
central bankers. Intuitively, during periods when society cares most
about stimulating the economy, the authorities do too. However, since
the authorities' preferences are not perfectly correlated with the
public's preferences, the public will be, on average, surprised by
expansions during these periods.

Since greater obfuscation of policy allows central banks to carry
out these surprise expansions, social planners may actually prefer
greater ambiguity in the form of greater monetary noise. More formally,
differentiating (17) with respect to [[sigma].sub.[phi]] demonstrates
that whether the social planners directly prefer more secrecy depends
upon which of two effects dominates. An increase in the degree of noise
improves their welfare since monetary authorities will conduct surprise
expansions when society most desires them. However, an increase in the
variance of the monetary control noise makes people pay less attention
to the money supply when making forecasts, thereby reducing the
authorities' ability to conduct surprise inflation in the first
place. Overall, when the benefits to unanticipated policy dominate the
loss in information from the money supply, society will prefer to be
less informed about policy intentions.

V. CONCLUDING REMARKS

This paper has presented two examples that explain why societies
allow central banks to remain secretive about their policy intentions.
First, when social planners prefer stable policy but monetary
authorities respond to the changing influence of interest groups, these
planners can induce the central bankers to smooth the monetary policy
process through institutions that promote greater policy persistence.
However, this action also increases the monetary authorities'
incentive to choose a policy process with greater noise and, therefore,
more secrecy. Since members of society recognize this incentive, they
prefer to choose institutions that appear to allow greater secrecy.
Second, when the social planners' own relative trade-offs change
over time, society may directly prefer that the central bank maintain
secrecy so as to be surprised by monetary expansions during periods when
the public prefers more economic stimulation. Although the analysis in
this paper has investigated these two extreme motivations for central
bank secrecy, the actual reasons are likely to be a combination of both
factors.

APPENDIX Results in the Text

Showing the results stated in the text depends upon the following
facts.

The first part is immediately obvious since sign([partial
derivative]a/[partial derivative]/ [B.sub.1]) =
sign([[sigma].sup.2.sub.[phi]] - [B.sup.2.sub.1] [[sigma].sup.2.sub.v])
For the second part, note that if ([partial derivative]a/[partial
derivative][B.sub.1]), then:

Proof: Since (da/d[theta]) = ([partial derivative]a/ [partial
derivative][theta])(d[B.sub.1]/d[theta]), substitute the definition of
a([B.sub.1]) from equation (7) into the equilibrium condition (10b) and
totally differentiate with respect to B and [theta]. Part (i) holds
since

(i) When [[sigma].sup.2.sub.[theta]] > [A.sup.2]. Since
([B.sub.1]/ [B.sub.0])>1 and (da/d[[sigma].sub.[phi]]) < 0 by fact
1, we have the result that (dE([W.sub.t])/d[[sigma].sub.[phi]]) > 0
at every equilibrium level of [B.sub.1] and [B.sub.0]. Therefore, the
highest possible noise variance is optimal.

(ii) When [[sigma].sup.2.sub.[theta]] < [A.sup.2], the optimal
value of [[sigma].sub.[phi]] is where
(dE([W.sub.t])/d[[sigma].sub.[phi]]) = 0, as can be verified by checking
the second-order conditions. Solving the first-order condition in terms
of [B.sub.1] implies

Proof to Result 3. The total differential of (13), society's
preferences, from a change in persistence is given by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

From result 1, [dE(U)/d[theta]] |[[sigma].sub.[phi]], > 0, so that
welfare is always increasing in [theta]. However, also by result 1,
(d[[sigma].sup.*.sub.[phi]]/d[phi]) > 0. Differentiating equation
(13) with respect to [[sigma].sub.[phi]] implies

where again K [equivalent to] (A/[[sigma].sub.v]). From fact
*********, so that (dE(U)/d[[sigma].sub.[phi]] < 0. Therefore,
society would prefer a lower level of persistence in policy objectives
than when (d[[sigma].sup.*.sub.[phi]]/d[theta]) = 0.

REFERENCES

Alt, James E. "Leaning Into the Wind or Ducking Out of the
Storm? U.S. Monetary Policy in the 1980s," in The Political Economy
of the Eighties, edited by A. Alesina and G. Carliner. Cambridge:
National Bureau of Economic Research, 1990.

Mayer, Thomas. "Disclosing Monetary Policy." Monograph
Series in Finance and Economics, Salomon Brothers Center for the Study
of Financial Institutions, New York University, 1987.

Rogoff, Kenneth. "The Optimal Degree of Commitment to an
Intermediate Monetary Target." Quarterly Journal of Economics,
November 1985, 1169-89.

Wooley, John T. The Federal Reserve and the Politics of Monetary
Policy. Cambridge: Cambridge University Press, 1984.

(1.) See Mayer [1987] on the evolution of disclosure requirements
of Federal Reserve policy in the U.S.

(2.) See Goodfriend [1986] on Merrill vs. the FOMC.

(3.) On the symbiotic relationship between these groups in forming
monetary policy, see Air [1990], Havrilesky [1988], and Wooley [1984].

(4.) In a related issue, Rogoff [1985] shows that society would
prefer a central banker with relatively more conservative preferences.

(5.) A similar issue is the effects of central bank independence
upon the economy. On this issue, see Alesina [1989] and Alesina and
Summers [1990].

(6.) For example, as a lawsuit was threatening to force the Fed to
publish the minutes of the FOMC meetings immediately following each
meeting, the Fed decided to abolish the minutes altogether. See Mayer
[1987, 13-15; 38-62].

(7.) This result reverses the causality to the argument in
Cukierman and Mettzer [1986a] that central bankers prefer secrecy in
order to surprise the money supply in periods when they care most about
increasing output. Here, members of society prefer to be surprised by
their own central banks.

(8.) See, for example, Cukierman and Meltzer [1986a; 1986b].

(9.) Since the basic structure is a simplified version of the
Cukierman and Meltzer [1986a] discretionary equilibrium, readers
familiar with this model may wish to skim through to section III below.

(10.) The effects of unemployment and inflation upon public
opinion about the state of the economy has been studied by Fischer and
Huizinga [1982]. The effects upon the popularity of the President is
documented in Frey and Schneider [1978]. Havrilesky [1987] considers the
effect upon the money supply of changes in government and social
expenditures.

(11.) That is, the ratio of the variance of [p.sub.t+1]
conditional upon [p.sub.t] over the total variance of [p.sub.t+1] equals
var[E([p.sub.t+1] | [p.sub.t])]/var([p.sub.t+1]) which equals
[theta]/(1+[theta]).

(12.) If [v.sub.t] were never observed, then the forecast of
policy objectives the following period would depend upon an infinite
backward-looking series of the information set. Intuitively, agents
would use the entire past history of the information in money to arrive
at an estimate of [v.sub.t-1]. In a similar vein, Cukierman and Meltzer
[1986a] treat the policy process as an auto-regressive process where the
innovations are never observed, so that agents must use an infinite
ordered backward-filter to forecast future policy. Although these two
specifications may add some realism to the discretionary equilibrium,
the assumption in the text does not alter any of the basic results
concerning central bank secrecy below.

(13.) Algebraically this conditional variance is {[B.sup.2.sub.1]
+ [[theta].sup.2] [[1 - a([B.sub.1])[B.sub.1].sup.2]}
[[sigma].sup.2.sub.v] - a[([B.sub.1]).sup.2][[theta].sup.2]
[[sigma].sup.2.sub.[phi]] and thus depends upon the parameters, [theta],
[[sigma].sub.v], and [[sigma].sub.[theta]]. Since the variability of
monetary noise and persistence in policy will be the focus of the
analysis below, the variability of policy preferences are subsumed in
equation (11).

(14.) These individuals comprise only an infinitesimal fraction of
overall society so that their preferences do not appear in the social
objective function (12). The case where these groups are large enough to
affect social welfare appears in section IV below.

(15.) In a similar vein, Alesina and Cukierman [1990] demonstrate
why politicians may prefer to be ambiguous about their true political
views.

KAREN K. LEWIS, University of Pennsylvania, New York University, and
NBER. For useful comments, I am grateful to three anonymous referees, to
Richard Sweeney, the co-editor, and to Alberto Alesina, Martin Evans,
Jim Lothian, Thomas Mayer, Guido Tabellini, and participants at seminars
at Carnegie Mellon University and New York University. Much of the work
in this paper was completed while I was a Visiting Scholar at the
Federal Reserve Board of Governors and was an Olin Foundation Fellow at
the National Bureau of Economic Research. All opinions and any errors
are mine alone.

COPYRIGHT 1991 Western Economic Association International
No portion of this article can be reproduced without the express written permission from the copyright holder.